To determine which ordered pairs are solutions to the system of linear inequalities, we will check each pair against both inequalities:
- Inequality 1: \(x + 2y \geq 10\)
- Inequality 2: \(3x - 4y > 12\)
Now, we substitute each ordered pair into the inequalities.
A. (16, 9)
- For Inequality 1: \(16 + 2(9) = 16 + 18 = 34 \geq 10\) (True)
- For Inequality 2: \(3(16) - 4(9) = 48 - 36 = 12 > 12\) (False)
B. (10, 2)
- For Inequality 1: \(10 + 2(2) = 10 + 4 = 14 \geq 10\) (True)
- For Inequality 2: \(3(10) - 4(2) = 30 - 8 = 22 > 12\) (True)
C. (8, 1)
- For Inequality 1: \(8 + 2(1) = 8 + 2 = 10 \geq 10\) (True)
- For Inequality 2: \(3(8) - 4(1) = 24 - 4 = 20 > 12\) (True)
D. (2, 6)
- For Inequality 1: \(2 + 2(6) = 2 + 12 = 14 \geq 10\) (True)
- For Inequality 2: \(3(2) - 4(6) = 6 - 24 = -18 > 12\) (False)
E. (4, -4)
- For Inequality 1: \(4 + 2(-4) = 4 - 8 = -4 \geq 10\) (False)
- For Inequality 2: \(3(4) - 4(-4) = 12 + 16 = 28 > 12\) (True)
F. (14, -1)
- For Inequality 1: \(14 + 2(-1) = 14 - 2 = 12 \geq 10\) (True)
- For Inequality 2: \(3(14) - 4(-1) = 42 + 4 = 46 > 12\) (True)
G. (-4, 2)
- For Inequality 1: \(-4 + 2(2) = -4 + 4 = 0 \geq 10\) (False)
- For Inequality 2: \(3(-4) - 4(2) = -12 - 8 = -20 > 12\) (False)
Now, let's summarize which points satisfy both inequalities:
- A: False
- B: True
- C: True
- D: False
- E: False
- F: True
- G: False
The ordered pairs that are solutions to the system of inequalities are:
B. (10, 2)
C. (8, 1)
F. (14, -1)
Therefore, the correct answers are B, C, and F.